How to keep dense particles at the center of emitter in blender 2.8?
So as stated in a comment, you can have two particle systems.

One (in green here) is the "outer" system. The other one (in red) the "inner" system.

By giving different lifetimes and initial velocities to your systems, you can probably approach your desired result.



Green is long lived with high velocity



Red/inner is short lived and with low velocity